Question

For what values of $n$ is true (where $n$ is a natural number)? the following statements are $5^n+4^n$ is divisible by $9$.

• A. All values of $n$
• B. Even values of $n$
• C. Odd values of $n$
• D. Cannot say

Answer 1

The correct option is C Odd values of $n$

$5^n+4^n$ is divisible by 9.
last digit of $5^n=5$
last digit of $4^n=4$ [for odd values of n] and
$6$ [for even values of n].
Now,$5^n+4^n$ is divisible by 9 only if last digit of $4^n$is 4
$\therefore 5^n+4^n$ is divisible by 9 for odd values of n.